Home
Class 12
MATHS
"If " int xlog(1+1//x)dx=f(x)log(x+1)+g(...

`"If " int xlog(1+1//x)dx=f(x)log(x+1)+g(x)x^(2)+Ax+C,` then

A

`f(x)=(1)/(2)x^(2)`

B

`g(x)=logx`

C

`A=1`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
d
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|61 Videos
  • INCREASING AND DECREASING FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|18 Videos
  • INVERSE TRIGONOMETRIC FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

Similar Questions

Explore conceptually related problems

Ifintxlog(1+1/x)dx=f(x)log(x+1)+g(x)x^2+A x+C , then (a) f(x)=1/2x^2 (b) g(x)=logx (c) A=1 (d) none of these

Ifintxlog(1+1/x)dx=f(x)log(x+1)+g(x)x^2+A x+C , then f(x)=1/2x^2 (b) g(x)=logx A=1 (d) none of these

int ln(1+x)^(1+x)dx

If int x log (1+x^(2))dx= phi (x) log (1+x^(2))+x(Psi)+C , then

If intx log (1+(1)/(x))dx =f(x).log_(e)(x+1)+g(x)log_(e)x+Lx+C , then

If int[(logx-1)/(1+(logx)^2)]^2dx=f(x)/(1+(g(x))^2)+c , then (A) f(x)=x (B) f(x)=x^2 (C) g(x)=logx (D) g(x)=(logx)^2

int(1)/(x(3+log x))dx

If int log(sqrt(1-x)+sqrt(1+x))dx=xf(x)+Ax+Bsin^(-1)x+C , then

int_(0)^(1)x log (1+2 x)dx

int (dx)/((x+1)(x-2))=A log (x+1)+B log (x-2)+C , where

OBJECTIVE RD SHARMA ENGLISH-INDEFINITE INTEGRALS-Chapter Test
  1. The integral int (2x-3)/(x^2+x+1)^2 .dx is equal to

    Text Solution

    |

  2. If int(xtan^(-1)x)/sqrt(1+x^(2))dx = sqrt(1+x^(2))f(x) + A " ln "sqrt(...

    Text Solution

    |

  3. "If " int xlog(1+1//x)dx=f(x)log(x+1)+g(x)x^(2)+Ax+C, then

    Text Solution

    |

  4. If int(xe^(x))/(sqrt(1+e^(x)))dx=f(x)sqrt(1+e^(x))-2logg(x)+C, then

    Text Solution

    |

  5. The value of int (cos^3x+cos^5)/(sin^2x+sin^4x)dx

    Text Solution

    |

  6. If int(dx)/((x^(2)+1)(x^(2)+4))=k tan^(-1) x + l tan^(-1) . (x)/(2) +C...

    Text Solution

    |

  7. If int log(sqrt(1-x)+sqrt(1+x))dx=xf(x)+Ax+Bsin^(-1)x+C, then

    Text Solution

    |

  8. If int(x^(5))/(sqrt(1+x^(3)))dx is equal to

    Text Solution

    |

  9. The value of : inte^(secx).sec^(3)x(sin^(2)x+cosx+sinx+sinxcosx)dx i...

    Text Solution

    |

  10. If int(2x^(2)+3)/((x^(2)-1)(x^(2)+4))dx=aln((x-1)/(x+1))+btan^(-1).(x)...

    Text Solution

    |

  11. Let f(x)=(x)/((1+x^(n))^(1//n)) for n ge 2 and g(x)=underset("n times"...

    Text Solution

    |

  12. The value of int ((ax^(2)-b)dx)/(xsqrt(c^(2)x^(2)-(ax^(2)+b)^(2))) is ...

    Text Solution

    |

  13. Evalaute: inte^(x)(1+nx^(n-1)-x^(2n))/((1-x^(n))sqrt(1-x^(2n))dx

    Text Solution

    |

  14. int(xcosx+1)/(sqrt(2x^(3)e^(sinx)+x^(2)))dx

    Text Solution

    |

  15. int(x^(3))/((1+x^(2))^(1//3))dx is equal to

    Text Solution

    |

  16. int sinx/sin(x-alpha)dx=Ax+B log (sin(x-alpha))+C then find out (A ,B)

    Text Solution

    |

  17. What is int (x^(2) +1)/(x^(4) - x^(2) + 1) dx equal to ?

    Text Solution

    |

  18. Evaluate: int(x-1)/((x+1)sqrt(x^3+x^2+x))dx

    Text Solution

    |

  19. int(1+x^(2))/(xsqrt(1+x^(4)))dx is equal to

    Text Solution

    |

  20. int(1+x^(4))/((1-x^(4))^(3//2))dx is equal to

    Text Solution

    |